He then inexplicably states that, even though you might disagree, the correct answer is actually 5!

Explanation?

Spoiler

Though I find such a puzzle to have some cleverness, the problem is with punctuation. It is missing. The sentence might should end with one or more additional exclamation points, implying emphasis, even though the initial ! character would be the factorial. Of course, the sentence should also be phrased differently. The verb "states" implies that the sentence should end in a full stop (period). This word might should be replaced with "exclaims" to support the additional one or more exclamation points that is suggested.